1. Field of the Invention
The present invention relates to a method of evaluating precision of output data using error propagation, particularly to a method of evaluating precision of output data using error propagation suitable for estimating uncertainty of a coordinate measurement value of a three-dimensional coordinate measuring machine (hereinafter simply referred to as a three-dimensional measuring machine or CMM).
2. Description of Related Art
In light of quality assurance, estimation of uncertainty is required for measurement results of any measurement equipment.
It is important in this regard to evaluate how precise calculation results are of complex data processing, simulations, and the like (hereinafter referred to as data processing). In the data processing, output data, which is the calculation results, is obtained based on input for calculation, such as input data, input parameters required for calculation processing, and the like (hereinafter parameters are included in input data). How much error is included the output data largely depends on how correct a calculation method or model is, based on which the data processing is performed. Even in a case in which the calculation method or model is sufficiently correct and thus correct output data can be obtained from correct input data, however, the output data has errors because of errors included in the input data. Hereinafter, data processing is assumed in which correct output data is obtained from correct input data.
Conventionally under the conditions above, an impact on the output data is observed by simply changing the input data (including parameters) by a slight amount; the output error is estimated by changing the input data with Monte Carlo simulation or experimental design; or the output data error is evaluated based on experience.
The importance of coordinate measurement using three-dimensional measuring machines has recently been increasing, in particular, in shape measurement in precision measurement. An actual shape is calculated in a least squares method, based on a plurality of measurement points measured on a shape by a three-dimensional measuring machine. In addition to uncertainty of the three-dimensional measuring machine itself, however, uncertainty changes according to measured objects, measurement environments, measurement strategies, and the like, thus making it difficult to correctly estimate the uncertainty.
The uncertainty of measurement results of three-dimensional measuring machines has conventionally been estimated in an experimental method, a method of a series of experiments, and a virtual CMM method (Monte Carlo simulation method) (refer to Related Arts 1 through 9).
[Related Art 1] Japanese Patent Laid-open Publication No. 2006-215011
[Related Art 2] Takamasu, Kiyoshi, Introduction to Three-Dimensional Coordinate Measurement—Precision Measurement Conditions and Uncertainty of Three-Dimensional Coordinate Measurement, “Method That Makes a Difference in Utilizing Three-Dimensional Coordinate Measurement Machines,” The Japan Society for Precision Engineering Seminar (December 2007)
[Related Art 3] Takamasu, Kiyoshi, Verification Method Based on GPS (Geometrical Product Specifications)—Interpreting Geometric Tolerance and Evaluating Uncertainty of Three-Dimensional Coordinate Measurement Machines, Design Engineering, 40 (2) (2005) pp. 79-85
[Related Art 4] Takamasu, Kiyoshi, Method of Estimating Uncertainty of Three-Dimensional Coordinate Measurement Machines and Its International Standardization, Machines and Tools, 45 (3) (2001) pp. 66-70
[Related Art 5] Takamasu, Kiyoshi, Osamu Sato, Ken Shimojima, Ryoshu Furutani, Artifact Calibration of Coordinate Measurement Machines (Report 3)—Estimating Uncertainty of Measurement After Calibration, Journal of the Japan Society for Precision Engineering, 71 (7) (2005) pp. 890-894
[Related Art 6] Takamasu, Kiyoshi, Makoto Abbe, Ryoshu Furutani, Shigeo Ozono, Estimating Uncertainty in Shape Measurement (Report 1)—Contribution of Systematic Error Caused in Calibration, Journal of the Japan Society for Precision Engineering, 67 (1) (2001) pp. 91-95
[Related Art 7] Takamasu, Kiyoshi, Makoto Abbe, Ryoshu Furutani, Shigeo Ozono, Estimating Uncertainty in Shape Measurement (Report 3)—Shape Deviation Model of Linear Bodies with Piecewise Polynomial, Journal of the Japan Society for Precision Engineering, 71 (11) (2005) pp. 1,454-1,458
[Related Art 8] Takamasu, Kiyoshi, Kenichiro Nosaka, Makoto Abbe, Ryoshu Furutani, Shigeo Ozono, Estimating Uncertainty in Shape Measurement (Report 2)—Contribution of Shape Deviation in Measuring Circular Bodies, Journal of the Japan Society for Precision Engineering, 69 (5) (2003) pp. 693-697
[Related Art 9] Takamasu, Kiyoshi, Ryoshu Furutani, Shigeo Ozono, Statistical Evaluation in Coordinate Measurement in Minimum Zone Method, Journal of the Japan Society for Precision Engineering, 64 (4) (1998) pp. 557-561
Among the methods above, however, it is difficult to efficiently generate input data that include errors in a Monte Carlo simulation. Further, its calculation load is high and reliability of results is low. Other methods are not used as general evaluation methods due to experimental aspects.
For complex measurement machines, such as three-dimensional measurement machines in particular, an effective method of estimating uncertainty has yet to be established in reality because of difficulty in estimating uncertainty, cost and time of experiments, and low estimation precision.